An Infinite-Server System with Lévy Shot-Noise Modulation: Moments and Asymptotics

We consider an infinite-server system with as input process a non-homogeneous Poisson process with rate function Λ(t) = a^⊺ X(t). Here {X(t): t ≥ 0} is a generalized multivariate shot-noise process fed by a Lévy subordi-nator rather than by just a compound Poisson process. We study the transient behavior of the model, analyzing the joint distribution of the number of cus-tomers in the queueing system jointly with the multivariate shot-noise process. We also provide a recursive procedure that explicitly identifies transient as well as stationary moments and correlations. Various heavy-tail and heavy-traffic asymptotic results are also derived, and numerical results are presented to provide further insight into the model behavior.